Permutation and combination problems play a major role in quantitative aptitude test. It is bit difficult to score marks in competitive exams without knowing the shortcuts related to permutation and combination problems. We might have already learned this topic in our school. Even though we have been already taught this topic in our higher classes in school, we need to learn some more short cuts which are being used to solve problems on this topic.
The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.
The ways of arranging or selecting smaller or equal number of persons or objects from a group of persons or collection of objects with due regard being paid to the order of arrangement or selection are called permutations.
The number of ways in which smaller or equal number of things are arranged or selected from a collection of things where the order of selection or arrangement is not important are called combinations
Difference between Permutations and Combinations:
Permutations : Selection is made. Beyond selection, order or arrangement is important.
Combinations : Selection is made. But order or arrangement is not important
Permtations : nPr = n!/(n-r)!
Combinations : nCr = n!/r!(n-r)!
Circular Permutations : = (n-1)!
(Both clockwise and anti clockwise rotations are considered. Hint: Every person has the same two neighbors)
Circular Permutations : = [(n-1)!]/2
(Either clockwise or anti clockwise rotation is considered.Not both. Hint: No person has the same two neighbors)
1. nPr = n(n-1)(n-2)....to "r" terms
Example: 7P3 = 7X6X5 = 210
2. nCr = [n(n-1)(n-2)...to "r" terms]/r!
Example: 7P3 = [7X6X5]/[3X2X1] =35
3. nCr = nCn-r (we will use this property only when we
want to reduce the value of "r")
Example: 25P22 = 25P3
4. nP1 = n
5. nC1 = n
6. nP0 = 1
7. nC0 = 1
8. nPn = n! (No. of permutations of n things taken all at a time)
9. nCn = 1
10. No. of Permutations of n things taken all at a time = (n-1)!.2!
(when two things always come together)
11. No. of Permutations of n things taken all at a time
= n!-(n-1)!.2! (when two things always not to come together)
12. The value of 0! = 1
12. Fundamental principle of counting:
AND ===> Multiplication, OR ===> Addition
Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from the topic permutations and combinations problems. Whether a person is going to write placement exam to get placed or a students is going to write a competitive exam in order to get admission in university, they must be prepared to solve permutation and combination problems. This is the reason for why people must study this topic.
Here, we are going to have some permutation and combination problems such that how shortcuts can be used. You can check your answer online and see step by step solution.
1. Compute the sum of all 4 digit numbers which can be formed with the digits 1, 3, 5, 7, if each digit is used only once in each arrangement.